Finite Group Databasebeta

?

← Prev (#44530386) Next (#44530388) →

D₁₅₆₂₃ #44530387

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 936 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,936)(20,935)(21,934)(22,933)(23,932)(24,931)(25,930)(26,929)(27,928)(28,927)(29,926)(30,925)(31,924)(32,923)(33,922)(34,921)(35,920)(36,919)(37,918)(38,917)(39,916)(40,915)(41,914)(42,913)(43,912)(44,911)(45,910)(46,909)(47,908)(48,907)(49,906)(50,905)(51,904)(52,903)(53,902)(54,901)(55,900)(56,899)(57,898)(58,897)(59,896)(60,895)(61,894)(62,893)(63,892)(64,891)(65,890)(66,889)(67,888)(68,887)(69,886)(70,885)(71,884)(72,883)(73,882)(74,881)(75,880)(76,879)(77,878)(78,877)(79,876)(80,875)(81,874)(82,873)(83,872)(84,871)(85,870)(86,869)(87,868)(88,867)(89,866)(90,865)(91,864)(92,863)(93,862)(94,861)(95,860)(96,859)(97,858)(98,857)(99,856)(100,855)(101,854)(102,853)(103,852)(104,851)(105,850)(106,849)(107,848)(108,847)(109,846)(110,845)(111,844)(112,843)(113,842)(114,841)(115,840)(116,839)(117,838)(118,837)(119,836)(120,835)(121,834)(122,833)(123,832)(124,831)(125,830)(126,829)(127,828)(128,827)(129,826)(130,825)(131,824)(132,823)(133,822)(134,821)(135,820)(136,819)(137,818)(138,817)(139,816)(140,815)(141,814)(142,813)(143,812)(144,811)(145,810)(146,809)(147,808)(148,807)(149,806)(150,805)(151,804)(152,803)(153,802)(154,801)(155,800)(156,799)(157,798)(158,797)(159,796)(160,795)(161,794)(162,793)(163,792)(164,791)(165,790)(166,789)(167,788)(168,787)(169,786)(170,785)(171,784)(172,783)(173,782)(174,781)(175,780)(176,779)(177,778)(178,777)(179,776)(180,775)(181,774)(182,773)(183,772)(184,771)(185,770)(186,769)(187,768)(188,767)(189,766)(190,765)(191,764)(192,763)(193,762)(194,761)(195,760)(196,759)(197,758)(198,757)(199,756)(200,755)(201,754)(202,753)(203,752)(204,751)(205,750)(206,749)(207,748)(208,747)(209,746)(210,745)(211,744)(212,743)(213,742)(214,741)(215,740)(216,739)(217,738)(218,737)(219,736)(220,735)(221,734)(222,733)(223,732)(224,731)(225,730)(226,729)(227,728)(228,727)(229,726)(230,725)(231,724)(232,723)(233,722)(234,721)(235,720)(236,719)(237,718)(238,717)(239,716)(240,715)(241,714)(242,713)(243,712)(244,711)(245,710)(246,709)(247,708)(248,707)(249,706)(250,705)(251,704)(252,703)(253,702)(254,701)(255,700)(256,699)(257,698)(258,697)(259,696)(260,695)(261,694)(262,693)(263,692)(264,691)(265,690)(266,689)(267,688)(268,687)(269,686)(270,685)(271,684)(272,683)(273,682)(274,681)(275,680)(276,679)(277,678)(278,677)(279,676)(280,675)(281,674)(282,673)(283,672)(284,671)(285,670)(286,669)(287,668)(288,667)(289,666)(290,665)(291,664)(292,663)(293,662)(294,661)(295,660)(296,659)(297,658)(298,657)(299,656)(300,655)(301,654)(302,653)(303,652)(304,651)(305,650)(306,649)(307,648)(308,647)(309,646)(310,645)(311,644)(312,643)(313,642)(314,641)(315,640)(316,639)(317,638)(318,637)(319,636)(320,635)(321,634)(322,633)(323,632)(324,631)(325,630)(326,629)(327,628)(328,627)(329,626)(330,625)(331,624)(332,623)(333,622)(334,621)(335,620)(336,619)(337,618)(338,617)(339,616)(340,615)(341,614)(342,613)(343,612)(344,611)(345,610)(346,609)(347,608)(348,607)(349,606)(350,605)(351,604)(352,603)(353,602)(354,601)(355,600)(356,599)(357,598)(358,597)(359,596)(360,595)(361,594)(362,593)(363,592)(364,591)(365,590)(366,589)(367,588)(368,587)(369,586)(370,585)(371,584)(372,583)(373,582)(374,581)(375,580)(376,579)(377,578)(378,577)(379,576)(380,575)(381,574)(382,573)(383,572)(384,571)(385,570)(386,569)(387,568)(388,567)(389,566)(390,565)(391,564)(392,563)(393,562)(394,561)(395,560)(396,559)(397,558)(398,557)(399,556)(400,555)(401,554)(402,553)(403,552)(404,551)(405,550)(406,549)(407,548)(408,547)(409,546)(410,545)(411,544)(412,543)(413,542)(414,541)(415,540)(416,539)(417,538)(418,537)(419,536)(420,535)(421,534)(422,533)(423,532)(424,531)(425,530)(426,529)(427,528)(428,527)(429,526)(430,525)(431,524)(432,523)(433,522)(434,521)(435,520)(436,519)(437,518)(438,517)(439,516)(440,515)(441,514)(442,513)(443,512)(444,511)(445,510)(446,509)(447,508)(448,507)(449,506)(450,505)(451,504)(452,503)(453,502)(454,501)(455,500)(456,499)(457,498)(458,497)(459,496)(460,495)(461,494)(462,493)(463,492)(464,491)(465,490)(466,489)(467,488)(468,487)(469,486)(470,485)(471,484)(472,483)(473,482)(474,481)(475,480)(476,479)(477,478)

Polycyclic presentation:

2,17,919|b^a=b^16,c^a=c^918

Conjugacy classes & character table

7813 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31246, 5);